Filter banks usually perform some kind of transformation between different domain signals, e.g. between time domain signals and frequency domain signals. Filter banks may have different structures and different individual output signal domains. In many cases, translation between different filter bank domains is desirable.
The European patent application EP06120969 discloses a method and device for transcoding between encoding formats with different time-frequency analysis domains, without using the time domain, wherein linear mapping is used. Thus, only a single transcoding step needs to be performed and computation complexity is lower than with systems that use intermediate time domain signals. One of the most important embodiments disclosed in EP06120969 is the mapping from the MP3 hybrid filter bank to the Integer MDCT domain for lossless audio compression. The transcoding step has significant influence on the compression ratio of the codec. A straight-forward solution for this mapping would be to fully decode the source filter coefficients from the MP3 domain into time domain samples, and then to apply the MDCT analysis filter bank. The solution provided in EP06120969 is to apply direct mapping from the MP3 filter bank domain to the MDCT domain, omitting the time domain. In this method, a number of mapping matrices are used which are approximately diagonal, but which vary over frequency. Therefore, this straight-forward approach requires a significant amount of lookup tables.
The modified discrete cosine transform (MDCT) is a kind of Fourier transform that is based on the discrete cosine transform (DCT). It is advantageous due to its property of being lapped, since it is performed on consecutive frames, wherein subsequent frames overlap, and its good compression of signal energy. In MP3 codecs, the MDCT is applied to the output of a 32-band polyphase quadrature filter (PQF) bank. The MDCT filter output is usually post-processed by an alias reduction for reducing the typical aliasing of the PQF filter bank. Such combination of a filter bank with an MDCT is called hybrid filter bank or subband MDCT.
A problem to be solved is to reduce the size of the mapping matrices, or the corresponding lookup tables, so that more efficient implementations are possible.